import geopandas as gpd
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np

pd.set_option('display.max_columns', 500)

Lab 4: Fire Service Coverage Analysis - Maximal Covering Location Problem

For this lab we return to Fire Service Coverage seeking to assess tradeoffs in service against costs of maintaining different levels of stations.
Instead of covering all demand, the modeling approach tries to maximize the demand covered.
Specifically, we will employ the maximal covering location problem.
Instead of minimizing the number of facilities needed in a previous lab, we now introduce a parameter, $p$, representing a fixed number of facilities to keep in the system.

In Lab 4, there are three research questions we want to look into.

1. Does a change in demand representation impact the optimization results?
2. How can a service system be evaluated to prioritize demand maximization?
3. Can the analysis process be generalized in order to replicate the approach using different demand representations?

The coverage standard for this lab will be fixed at 8000m.

S = 8000

Step 1. Prepare your dataset

Task: Load the three datasets and convert blocks and stations crs into the same one as FDs.crs.

• It is because FDs is in a crs using meter as linear unit.

# Note: it might take time, as FD is a huge file.

FDs = gpd.read_file("/Users/ezrabanks/Desktop/Lab4/Data/California_Fire_Districts.shp")
blocks = gpd.read_file("/Users/ezrabanks/Desktop/Lab4/Data/sbBlocks_pop.shp")
stations = gpd.read_file("/Users/ezrabanks/Desktop/Lab4/Data/Fire_Stations_SBC.shp")

blocks = blocks.to_crs(crs = FDs.crs)
stations = stations.to_crs(crs = FDs.crs)

Task: Look into the following Fire District maps.

There are many Fire Districts in California.
We are only going to focus in the "Santa Barbara County Fire District".
In the second map, note that there are many other Fire Districts in Santa Barbara County.
Though it's not shown on the map, they have some overlapping area, which means the area is co-operated by multiple Fire Districts.

FDs.plot("Name")

<Axes: >

FDs = FDs.loc[FDs.intersects(blocks.unary_union)].reset_index(drop=True)
FDs.plot("Name", legend=True, figsize=(10,10))

<Axes: >

Question 1: Sort out a Fire District out of FDs GeoDataFrame. The district must have its 'Name" column value, "SANTA BARBARA CFD". ( 1 pt )

SBC_FD = FDs[FDs["Name"] == "SANTA BARBARA CFD"]

SBC_FD

	OBJECTID	County	FDID	MACSID	Name	Address	City	Zip	FireChief	Phone	Notes	LastUpdate	Website	CALFIREUni	SHAPE_Leng	SHAPE_Area	geometry
4	318	SANTA BARBARA	42035	SBC	SANTA BARBARA CFD	4410 CATHEDRAL OAKS RD	SANTA BARBARA	93110	MARK A. HARTWIG	(805) 681‐5500	None	2018-06-21	https://www.sbcfire.com/	SBC	778360.396807	3.666998e+09	MULTIPOLYGON (((23728.804 -401033.857, 23715.3...

Task: Run following cell, "del FDs". Note: It will delete FDs variable.

We do this because FDs contains a large shapefile, which might burden your RAM.

del FDs

Task: take a subset of stations, within SBC_FD.

NOTE: don't forget to RESET_INDEX() whenever you take a subset!

stations = stations[stations.within(SBC_FD.geometry.unary_union)].reset_index(drop = True)

len(stations)

28

Question 2: Plot the blocks GeoDataFrame. ( 2 pts )

• Firstly, update the blocks GeoDataFrame's geometry column to have block centroids, not block polygons ( 0.5 pt )
• Secondly, take a subset of blocks which is within the SBC_FD area ( 0.5 pt )
• Thirdly, plot blocks GeoDataFrame with "Population" column. ( 1 pt )
  • figsize=(10,10)
  • opacity must be 0.4
  • take a cmap (colormap) that you like from this webpage (https://matplotlib.org/stable/users/explain/colors/colormaps.html).
  • markersize must be proportional to the column, "Population"
  • ensure you have legend
  • Plot with stations GeoDataFrame

Hint: when there's something you don't know about plot function, refer to this document page (https://geopandas.org/en/stable/docs/reference/api/geopandas.GeoDataFrame.plot.html)! Also, you can Google or ask chatGPT :)

blocks['geometry'] = blocks['geometry'].centroid

blocks = blocks[blocks.within(SBC_FD.geometry.unary_union)].reset_index(drop = True)

fig, ax = plt.subplots(figsize=(10, 10))
blocks.plot(column='Population', ax=ax, legend=True, cmap = 'viridis', figsize = fig, alpha = 0.4, markersize=blocks['Population']*0.8)
stations.plot(ax=ax, color='red', label='Stations')

<Axes: >

len(blocks)

3224

len(stations)

28

Step 2. Conduct MCLP

Decision Variables: \begin{align*} & x_j = \begin{cases} 1, & \text{if facility $j$ is open}, \\ 0, & \text{otherwise}. \end{cases} \\ & y_i = \begin{cases} 1, & \text{if demand $i$ is covered}, \\ 0, & \text{otherwise}. \end{cases} \end{align*}

Parameters: \begin{align*} & I = \text{number of demands}, \\ & J = \text{number of facilities}, \\ & S = \text{Coverage Distance Standard}, \\ & a_i = \text{Weight assigned to demand $i$}, \\ & D_{ij} = \text{Distance between demand $i$ and facility $j$}, \\ & N_i = \{ j \in J \, | \, D_{ij} \leq S \}, \\ & P = \text{the number of facilities to be opened}. \end{align*}

Objective Function: \begin{align*} \text{Maximize:} \quad & \sum_{i=1}^{I} a_i y_i \end{align*}

Constraints: \begin{align*} \text{Subject to:} \quad & \sum_{j \in N_i} x_j \geq y_i, \quad \forall i \in I \\ & \sum_{j=1}^{J} x_j \leq P, \\ & x_j, y_i \in \{0, 1\}, \quad \forall i, j. \end{align*}

Task: Based on the mathematical Model, set the I and J values correctly.

• In this section, we will consider each block as demand $i$
• we will consider each existing fire station as facility $j$
• In the beginning of this lab, we defined our S value to be 8000 meter, 8 km.
• Pick any P that is less than current number of stations :)

I = len(blocks)
J = len(stations)
P = 20

Task: We are going to have block's population as weight assigned to demand. Define $a_i$.

a_i = blocks["Population"]

Task: Create $D_{ij}$ variable using Euclidean Distance between demand $i$ and facility $j$.

D_ij = np.array([[blocks.geometry[i].distance(stations.geometry[j]) for j in range(J)] for i in range(I)])
D_ij.shape

(3224, 28)

Question 3: Create $N_i$ variable in list format. ( 1 pt )

• Previously, $N_i$ in dictionary is introduced.
• With your understanding so far, list format of $N_i$ can also be created.
• You can use double for-loops, or list comprehension.

# This is a hint for students who want to do it with list comprehension


# Creating a two-dimensional list
matrix = [[1, 2, 3],
          [4, 5, 6],
          [7, 8, 9],
          [10, 11, 12]]

# Using list comprehension to filter even numbers from the matrix
# The '%' symbol in Python is called the modulo operator. 
    #It returns the remainder of the division of the left operand by the right operand.
even_numbers = [[matrix[r][c] for c in range(len(matrix[0])) if matrix[r][c]%2 == 0]
                for r in range(len(matrix))]

print(even_numbers)

[[2], [4, 6], [8], [10, 12]]

N_i = [[j for j in range(J) if D_ij[i][j] <= S] for i in range(I)]

Question 4: Complete the Optimization Model ( 6 pts )

import gurobipy as gp
from gurobipy import GRB

# Create a new Gurobi model
mclp = gp.Model("Maximal_Covering_Location")

# Decision Variables
x = mclp.addVars(I, vtype=gp.GRB.BINARY, name="x")
y = mclp.addVars(I, vtype=gp.GRB.BINARY, name="y")

# Objective Function
mclp.setObjective(gp.quicksum(a_i[i] * y[i] for i in range(I)), GRB.MAXIMIZE)

# Constraints
# Each demand must be covered by neighboring facility
mclp.addConstrs((gp.quicksum(x[j] for j in N_i[i]) >= y[i] for i in range(I)))

# Number of opened facilities must not exceed P
mclp.addConstr(gp.quicksum(x[j] for j in range(J)) <= P)

# Optimize the model
mclp.optimize()

Set parameter Username
Academic license - for non-commercial use only - expires 2025-05-10
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x8394f29b
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.02s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

Question 5: Take a subset of stations based on the model output. ( 1 pt )

open_stations = [j for j in range(J) if x[j].X > 0.5]
open_stations = stations.iloc[open_stations].reset_index(drop=True)
open_stations

	Label	Desig	Number	Type	Department	Name_other	Address	Notes	Num_2019	Scale	Latitude	Longitude	geometry
0	VAFB-42	AFV-2	42	Fire Station	Vandenberg Fire Department	None	New Mexico Ave., Vandenberg, CA	None	42	0	34.7345	-120.534	POINT (-48865.923 -364526.814)
1	VAFB-44	AFV-4	44	Fire Station	Vandenberg Fire Department	None	Arguello Rd., Vandenberg, CA	None	44	0	34.6125	-120.570	POINT (-52227.109 -378048.804)
2	SBC-31	SBC-31	31	Fire Station	Santa Barbara County Fire Department	None	168 W Hwy 246, Buellton, CA 93427	None	31	900	34.6132	-120.197	POINT (-18043.064 -378107.359)
3	SBC-30	SBC-30	30	Fire Station	Santa Barbara County Fire Department	None	1644 Oak St., Solvang, CA 93464	None	30	900	34.5935	-120.142	POINT (-12980.623 -380307.178)
4	SBC-32	SBC-32	32	Fire Station	Santa Barbara County Fire Department	None	906 Airport Rd., Santa Ynez, CA 93460	None	32	1100	34.6075	-120.069	POINT (-6364.715 -378763.420)
5	SBC-13	SBC-13	13	Fire Station	Santa Barbara County Fire Department	None	4570 Hollister, Santa Barbara, CA 93110	None	13	1000	34.4386	-119.780	POINT (20241.872 -397479.331)
6	SBC-27	SBC-27	27	Fire Station	Santa Barbara County Fire Department	None	41 Newsome St., New Cuyama, CA 93254	None	27	700	34.9457	-119.682	POINT (29023.176 -341164.220)
7	LPF-35	LPF-35	35	Fire Station	LPF	Pine Canyon	8145 Hwy 166, Santa Maria, CA 93454	None	35	0	35.0294	-120.194	POINT (-17696.745 -331903.082)
8	SBC-23	SBC-23	23	Fire Station	Santa Barbara County Fire Department	None	5003 Depot Ave., Santa Maria, CA 93454	None	23	600	34.8666	-120.294	POINT (-26898.330 -349956.970)
9	SBC-24	SBC-24	24	Fire Station	Santa Barbara County Fire Department	None	99 Centennial, Los Alamos, CA 93440	None	24	800	34.7451	-120.280	POINT (-25603.519 -363453.395)
10	SBC-26	SBC-26	26	Fire Station	Santa Barbara County Fire Department	None	1600 Tiffany Park Court, Santa Maria, CA 93455	None	26	600	34.8657	-120.402	POINT (-36721.414 -350025.728)
11	SBC-21	SBC-21	21	Fire Station	Santa Barbara County Fire Department	None	335 Union Ave., Orcutt, CA 93455	None	21	600	34.8644	-120.444	POINT (-40540.132 -350149.951)
12	SBC-34	SBC-34	34	Fire Station	Santa Barbara County Fire Department	None	3510 Harris Grade Rd., Lompoc, CA 93436	None	34	1000	34.6909	-120.447	POINT (-40958.522 -369401.362)
13	VAFB-43	AFV-3	43	Fire Station	Vandenberg Fire Department	None	El Rancho Rd., Vandenberg, CA	None	43	0	34.7882	-120.565	POINT (-51640.364 -358544.456)
14	SBC-12	SBC-12	12	Fire Station	Santa Barbara County Fire Department	None	5330 Calle Real, Goleta, CA 93117	None	12	900	34.4429	-119.812	POINT (17256.190 -397008.608)
15	SBC-11	SBC-11	11	Fire Station	Santa Barbara County Fire Department	None	6901 Frey Way, Goleta, CA 93117	None	11	700	34.4258	-119.870	POINT (11934.816 -398917.392)
16	SBC-38	SBC-38	38	Fire Station	Santa Barbara County Fire Department	None	17200 Mariposa Reina, Gaviota, CA 93117	None	38	800	34.4767	-120.214	POINT (-19690.488 -393256.876)
17	SBC Camp 1	SBC-CR	None	Camp	Santa Barbara County Fire Department	Cachuma Camp	Lakeview Dr., Lake Cachuma, CA	Crew 10, Crew 11	CREW	1200	34.5688	-119.948	POINT (4737.414 -383052.783)
18	CHU-1	CHU-1	1	Fire Station	Chumash Fire Department	Chumash	3300 Hwy 246, Santa Ynez, CA 93460	None	1	0	34.6088	-120.089	POINT (-8141.257 -378616.310)

Question 6: Plot the open_stations and their coverage buffers with the demand buffers. ( 2 pts )

• Copy and Paste the plotting code from Question 2.
• Replace stations with open_stations.
• Add another plot function which plots the buffer with buffer distance S from each open_station.
  • The coverage buffer shouldn't have facecolor
  • Buffer Boundary must be dashed lines. (ask chatGPT of google how to do this!)

coverage_buffers = open_stations.geometry.buffer(S)
fig, ax = plt.subplots(figsize=(10, 10))
blocks.plot(column='Population', ax=ax, legend=True, cmap='viridis', alpha=0.4, markersize=blocks['Population']*0.8)
open_stations.plot(ax=ax, color='red', label='Open Stations')
SBC_FD.plot(ax=ax, markersize=5, zorder=2, facecolor="none", edgecolor="black")
coverage_buffers.plot(ax=ax, edgecolor='black', linestyle='--', linewidth=1, facecolor="none")

plt.legend()
plt.show()

Step 3. Functionize / Modularize

Here, we will functionize our optimization model.
Sothat with given P value, the model can be solved.

Question 7: Functionize your code out of Question 4 and 5 ( 2 pts )

• start defining a function named, "solve_mclp". ( 0.5 pts )
• The function takes one argument, P. ( 0.5 pts )
• Within the function, copy and paste the code you did for Question 4 and 5. ( 0.5 pts )
• Then, add the last line of code, to return open_stations, and mclp.obj_val ( 0.5 pts )

# Let me give you functionize example.
# For more, refer to Lab 0.

sample_list = [1,2,3,4]

def sum_array(a):
    s = 0
    a = np.array(a)
    for num in a:
        s += num
    return s, a # Return the summation of all elements, and the original array

sum_array(sample_list)

(10, array([1, 2, 3, 4]))

## PUT YOUR FUNCTION HERE!!!##
def solve_mclp(P):
    import gurobipy as gp
    from gurobipy import GRB

    # Create a new Gurobi model
    mclp = gp.Model("Maximal_Covering_Location")

    # Decision Variables
    x = mclp.addVars(I, vtype=gp.GRB.BINARY, name="x")
    y = mclp.addVars(I, vtype=gp.GRB.BINARY, name="y")

    # Objective Function
    mclp.setObjective(gp.quicksum(a_i[i] * y[i] for i in range(I)), GRB.MAXIMIZE)

    # Constraints
    # Each demand must be covered by neighboring facility
    mclp.addConstrs((gp.quicksum(x[j] for j in N_i[i]) >= y[i] for i in range(I)))

    # Number of opened facilities must not exceed P
    mclp.addConstr(gp.quicksum(x[j] for j in range(J)) <= P)

    # Optimize the model
    mclp.optimize()

    open_stations = [j for j in range(J) if x[j].X > 0.5]
    open_stations = stations.iloc[open_stations].reset_index(drop=True)
    
    return open_stations,mclp.obj_val

Step 4. Evaluate the Result

Question 8: To evaluate the optimization result, we always compare with the current operation. Calculate current_coverage. ( 2 pts )

Current coverage is the sum of all the demand weights, currently covered by existing stations.
Here are the thought process you can go through.

• Create buffers with distance S out of all the existing stations.
• Take a unary_union of the buffers. ( 0.5 pts )
• Use .within() function to take a subset of blocks, within the unary_union of coverage buffers. ( 0.5 pts )
• Take the Population column out of the subset of blocks. ( 0.5 pts )
• Take the sum of the column values. ( 0.5 pts )

current_coverage = open_stations.buffer(distance = S)
current_coverage = current_coverage.unary_union
current_coverage = blocks.within(current_coverage)
covered_blocks = blocks.loc[current_coverage]

covered_blocks_sum = covered_blocks["Population"].sum()
current_coverage = covered_blocks_sum
current_coverage

167606

current_coverage = stations.buffer(distance = S)
current_coverage = fishnet_points[fishnet_points.geometry.within(current_coverage.unary_union)].reset_index(drop=True)
sum_current = len(current_coverage)

Task: Check if provided code works with your defined function, solve_mclp

selecteds = []  # List to store selected stations for each value of p
obj_vals = []   # List to store objective values for each value of p

# Iterate over values of p starting from 3
for p in range(3, len(stations)+1):
    print(f"=================== for P={p}")  # Print current value of p
    # Call solve_mclp function to solve the problem for current value of p
    selected_stations, obj_val = solve_mclp(p)
    # Append selected stations to the selecteds list
    selecteds.append(selected_stations)
    # Append objective value to the obj_vals list
    obj_vals.append(obj_val)

=================== for P=3
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xfbb69dab
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 28463.000000

Root relaxation: objective 1.420460e+05, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    142046.00000 142046.000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 142046 28463 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.420460000000e+05, best bound 1.420460000000e+05, gap 0.0000%
=================== for P=4
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x74a1aab2
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 35944.000000

Root relaxation: objective 1.535990e+05, 20 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    153599.00000 153599.000  0.00%     -    0s

Explored 1 nodes (20 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 153599 35944 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.535990000000e+05, best bound 1.535990000000e+05, gap 0.0000%
=================== for P=5
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x41ce3697
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 101213.00000

Root relaxation: objective 1.578710e+05, 19 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    157871.00000 157871.000  0.00%     -    0s

Explored 1 nodes (19 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 157871 101213 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.578710000000e+05, best bound 1.578710000000e+05, gap 0.0000%
=================== for P=6
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x205c5f99
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 103347.00000

Root relaxation: objective 1.615640e+05, 16 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    161564.00000 161564.000  0.00%     -    0s

Explored 1 nodes (16 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 161564 103347 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.615640000000e+05, best bound 1.615640000000e+05, gap 0.0000%
=================== for P=7
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x9e88aae7
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 138503.00000

Root relaxation: objective 1.636980e+05, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    163698.00000 163698.000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 163698 138503 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.636980000000e+05, best bound 1.636980000000e+05, gap 0.0000%
=================== for P=8
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x6f496596
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139069.00000

Root relaxation: objective 1.656950e+05, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    165695.00000 165695.000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.09 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 165695 139069 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.656950000000e+05, best bound 1.656950000000e+05, gap 0.0000%
=================== for P=9
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xb870dc24
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139439.00000

Root relaxation: objective 1.663330e+05, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166333.00000 166333.000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 166333 139439 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.663330000000e+05, best bound 1.663330000000e+05, gap 0.0000%
=================== for P=10
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x1e198654
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139558.00000

Root relaxation: objective 1.668990e+05, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166899.00000 166899.000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 166899 139558 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.668990000000e+05, best bound 1.668990000000e+05, gap 0.0000%
=================== for P=11
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xce9ccc4f
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140196.00000

Root relaxation: objective 1.671390e+05, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167139.00000 167139.000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 167139 140196 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.671390000000e+05, best bound 1.671390000000e+05, gap 0.0000%
=================== for P=12
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x75c48cb7
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140425.00000

Root relaxation: objective 1.673330e+05, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167333.00000 167333.000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.08 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 167333 140425 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.673330000000e+05, best bound 1.673330000000e+05, gap 0.0000%
=================== for P=13
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xd97f63fc
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167360.00000

Root relaxation: objective 1.674520e+05, 2 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167452.00000 167452.000  0.00%     -    0s

Explored 1 nodes (2 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 167452 167360 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.674520000000e+05, best bound 1.674520000000e+05, gap 0.0000%
=================== for P=14
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x172f26d6
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.04s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167374.00000

Root relaxation: objective 1.675220e+05, 2 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167522.00000 167522.000  0.00%     -    0s

Explored 1 nodes (2 simplex iterations) in 0.14 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 167522 167374 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.675220000000e+05, best bound 1.675220000000e+05, gap 0.0000%
=================== for P=15
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xcd36c397
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167443.00000

Root relaxation: objective 1.675910e+05, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167591.00000 167591.000  0.00%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 167591 167443 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.675910000000e+05, best bound 1.675910000000e+05, gap 0.0000%
=================== for P=16
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x354d63a9
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167605.00000

Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 167605 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676050000000e+05, best bound 1.676050000000e+05, gap 0.0000%
=================== for P=17
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xe7e25a44
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3203 rows and 6407 columns
Presolve time: 0.02s
Presolved: 22 rows, 41 columns, 90 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 41 integer (41 binary)

Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.01 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=18
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x85b62fa8
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3210 rows and 6414 columns
Presolve time: 0.01s
Presolved: 15 rows, 34 columns, 62 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 34 integer (34 binary)

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.01 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=19
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xb50fdd7a
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=20
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x8394f29b
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.02s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=21
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x5da5f73e
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.02s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=22
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x25d04cef
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=23
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x0c7cae08
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=24
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x53d33e31
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=25
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x7ea4a4ef
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=26
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x5c8dcf4c
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=27
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x14058442
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.02s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=28
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x7fc3c448
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

Task: Check if the output Table is plausible. And learn how to create a pandas DataFrame

• To create a DataFrame, you can call pandas.DataFrame() and deliver a dictionary.
• The dictionary will have key and value pairs.
  • key will be the column name
  • value will be an array of column values

results = pd.DataFrame({
    'P': range(3, len(stations)+1),
    'Coverage': obj_vals
})
results

	P	Coverage
0	3	540.0
1	4	704.0
2	5	855.0
3	6	1005.0
4	7	1146.0
5	8	1270.0
6	9	1384.0
7	10	1475.0
8	11	1564.0
9	12	1647.0
10	13	1715.0
11	14	1743.0
12	15	1763.0
13	16	1780.0
14	17	1789.0
15	18	1793.0
16	19	1797.0
17	20	1797.0
18	21	1797.0
19	22	1797.0
20	23	1797.0
21	24	1797.0
22	25	1797.0
23	26	1797.0
24	27	1797.0
25	28	1797.0

current_coverage

4065

def scatterplot_result(results):
    # Plot the DataFrame, in scatter plot, taking P values as x and Coverage values as y
    results.plot(kind="scatter", x="P", y="Coverage")
    # Add grid lines
    plt.grid(True)
    # Add the current coverage point in color red
    plt.scatter(len(stations), sum_current, color="red")
    # provide a dashed red line to inform current coverage
    plt.axhline(y=sum_current, color='r', linestyle='--', label='Current Coverage')
    # show the plot!
    plt.show()
    
scatterplot_result(results)

Task: Put your code to plot open_stations and coverage buffer from Question 6.

Feel free to edit any other plotting details

def map_result(p, demand_block=True):
    
    ####My answer
    open_stations = selecteds[p-3]
    coverage_buffers = open_stations.geometry.buffer(S)
    fig, ax = plt.subplots(figsize=(10, 10))
    #blocks.plot(column='Population', ax=ax, legend=True, cmap='viridis', alpha=0.4, markersize=blocks['Population']*0.8)
    open_stations.plot(ax=ax, color='red', label='Open Stations', zorder = 5000)
    SBC_FD.plot(ax=ax, markersize=5, zorder=200, facecolor="none", edgecolor="black")
    coverage_buffers.plot(ax=ax, edgecolor='black', linestyle='--', linewidth=1, facecolor="none")

    #plt.legend()
    #plt.show()
    ####
    
    if demand_block:
        blocks.plot("Population", ax=ax, legend=True, markersize=5)
    else:
        fishnet_points.plot(ax=ax, zorder = 100)
    plt.title(f"{p} stations open")
    plt.show()
    
map_result(10) # Try different p!

Task: Following function is to go through the whole process. Check if you get the same output as before :)

def optimize_and_evaluate(demand_block=True):
    selecteds = [] 
    obj_vals = [] 
    for p in range(3, len(stations)+1):
        print(f"=================== for P={p}")
        selected_stations, obj_val = solve_mclp(p)
         selecteds.append(selected_stations)
        obj_vals.append(obj_val)
        map_result(p, demand_block)
        
    results = pd.DataFrame({
        'P': range(3, len(stations)+1),
        'Coverage': obj_vals
    })
    scatterplot_result(results)

optimize_and_evaluate()

=================== for P=3
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xfbb69dab
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 28463.000000

Root relaxation: objective 1.420460e+05, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    142046.00000 142046.000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 142046 28463 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.420460000000e+05, best bound 1.420460000000e+05, gap 0.0000%

=================== for P=4
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x74a1aab2
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 35944.000000

Root relaxation: objective 1.535990e+05, 20 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    153599.00000 153599.000  0.00%     -    0s

Explored 1 nodes (20 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 153599 35944 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.535990000000e+05, best bound 1.535990000000e+05, gap 0.0000%

=================== for P=5
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x41ce3697
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 101213.00000

Root relaxation: objective 1.578710e+05, 19 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    157871.00000 157871.000  0.00%     -    0s

Explored 1 nodes (19 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 157871 101213 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.578710000000e+05, best bound 1.578710000000e+05, gap 0.0000%

=================== for P=6
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x205c5f99
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 103347.00000

Root relaxation: objective 1.615640e+05, 16 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    161564.00000 161564.000  0.00%     -    0s

Explored 1 nodes (16 simplex iterations) in 0.08 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 161564 103347 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.615640000000e+05, best bound 1.615640000000e+05, gap 0.0000%

=================== for P=7
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x9e88aae7
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 138503.00000

Root relaxation: objective 1.636980e+05, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    163698.00000 163698.000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 163698 138503 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.636980000000e+05, best bound 1.636980000000e+05, gap 0.0000%

=================== for P=8
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x6f496596
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139069.00000

Root relaxation: objective 1.656950e+05, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    165695.00000 165695.000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 165695 139069 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.656950000000e+05, best bound 1.656950000000e+05, gap 0.0000%

=================== for P=9
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xb870dc24
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139439.00000

Root relaxation: objective 1.663330e+05, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166333.00000 166333.000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 166333 139439 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.663330000000e+05, best bound 1.663330000000e+05, gap 0.0000%

=================== for P=10
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x1e198654
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139558.00000

Root relaxation: objective 1.668990e+05, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166899.00000 166899.000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 166899 139558 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.668990000000e+05, best bound 1.668990000000e+05, gap 0.0000%

=================== for P=11
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xce9ccc4f
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140196.00000

Root relaxation: objective 1.671390e+05, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167139.00000 167139.000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 167139 140196 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.671390000000e+05, best bound 1.671390000000e+05, gap 0.0000%

=================== for P=12
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x75c48cb7
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140425.00000

Root relaxation: objective 1.673330e+05, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167333.00000 167333.000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 167333 140425 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.673330000000e+05, best bound 1.673330000000e+05, gap 0.0000%

=================== for P=13
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xd97f63fc
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167360.00000

Root relaxation: objective 1.674520e+05, 2 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167452.00000 167452.000  0.00%     -    0s

Explored 1 nodes (2 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 167452 167360 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.674520000000e+05, best bound 1.674520000000e+05, gap 0.0000%

=================== for P=14
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x172f26d6
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167374.00000

Root relaxation: objective 1.675220e+05, 2 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167522.00000 167522.000  0.00%     -    0s

Explored 1 nodes (2 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 167522 167374 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.675220000000e+05, best bound 1.675220000000e+05, gap 0.0000%

=================== for P=15
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xcd36c397
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167443.00000

Root relaxation: objective 1.675910e+05, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167591.00000 167591.000  0.00%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 167591 167443 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.675910000000e+05, best bound 1.675910000000e+05, gap 0.0000%

=================== for P=16
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x354d63a9
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167605.00000

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 167605 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676050000000e+05, best bound 1.676050000000e+05, gap 0.0000%

=================== for P=17
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xe7e25a44
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3203 rows and 6407 columns
Presolve time: 0.01s
Presolved: 22 rows, 41 columns, 90 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 41 integer (41 binary)

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.01 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

=================== for P=18
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x85b62fa8
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3210 rows and 6414 columns
Presolve time: 0.01s
Presolved: 15 rows, 34 columns, 62 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 34 integer (34 binary)

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.01 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

=================== for P=19
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xb50fdd7a
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.03s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

=================== for P=20
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x8394f29b
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

=================== for P=21
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x5da5f73e
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

=================== for P=22
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x25d04cef
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

=================== for P=23
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x0c7cae08
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

=================== for P=24
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x53d33e31
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

=================== for P=25
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x7ea4a4ef
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.10s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.12 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

=================== for P=26
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x5c8dcf4c
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

=================== for P=27
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x14058442
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

=================== for P=28
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x7fc3c448
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

Step 4. Replicate your Analysis with different Demand Representations

Task: Review from Lab 2. We are creating fishnet points within the SBC_FD

boundary = SBC_FD.envelope # .envelope gives you the bounding rectangle of given GeoDataFrame.
boundary.bounds

	minx	miny	maxx	maxy
4	-61331.613	-401270.1778	50847.5684	-323367.7559

minx, miny, maxx, maxy = boundary.loc[4].bounds
print(minx, miny, maxx, maxy)

-61331.61300000176 -401270.1777999997 50847.56839999929 -323367.7559000002

from shapely.geometry import Point

# Here, we are going to create fishnet points.
    # Fishnet points are points spaced with an equal interval.
    # You'll see when you see the output!

# Define the interval between points 
#### Note: Adjust interval value as needed for lab question 2
def create_fishnet(interval):
# Create arrays of x and y coordinates using np.arange
    x_coords = np.arange(minx, maxx, interval)
    y_coords = np.arange(miny, maxy, interval)

    # Create a list to store the points
    fishnet_points = []

    # Generate points for the fishnet
    for y in y_coords:
        for x in x_coords:
            fishnet_points.append((x, y))

    # Print the number of points generated
    print("Number of points in the fishnet:", len(fishnet_points))

    fishnet_points = gpd.GeoSeries([Point(pt_cd) for pt_cd in fishnet_points])
    fishnet_points = fishnet_points[fishnet_points.within(SBC_FD.geometry[4])]
    fishnet_points.plot(figsize=(15,5))
    return fishnet_points

interval = 5280/5  # default: 5280/5 feet (1 mile / 5 = 0.2 mile) 
fishnet_points = create_fishnet(interval)

Number of points in the fishnet: 7918

# Current Coverage
current_coverage = fishnet_points.within(stations.buffer(S).unary_union)
current_coverage = current_coverage.sum()
current_coverage

4065

Question 9: Re-compute the model variables here for fishnet_points, instead of blocks. ( 1 pt )

Note: all the fishnet points will have the same weight, 1.

I = len(fishnet_points)
J = len(stations)
a_i = [1 for i in fishnet_points]
D_ij = np.zeros((I, J))
for i in range (I):
    for j in range (J):
        D_ij[i][j] = fishnet_points.geometry.iloc[i].distance(stations.geometry.iloc[j])
N_i = {i: [j for j in range(J) if D_ij[i][j] <= S] for i in range(I)}

selecteds = []  # List to store selected stations for each value of p
obj_vals = []   # List to store objective values for each value of p

# Iterate over values of p starting from 3
for p in range(3, len(stations)+1):
    print(f"=================== for P={p}")  # Print current value of p
    # Call solve_mclp function to solve the problem for current value of p
    selected_stations, obj_val = solve_mclp(p)
    # Append selected stations to the selecteds list
    selecteds.append(selected_stations)
    # Append objective value to the obj_vals list
    obj_vals.append(obj_val)

=================== for P=3
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x389340da
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 506.0000000

Root relaxation: objective 5.400000e+02, 45 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     540.0000000  540.00000  0.00%     -    0s

Explored 1 nodes (45 simplex iterations) in 0.17 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 540 506 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 5.400000000000e+02, best bound 5.400000000000e+02, gap 0.0000%
=================== for P=4
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x7e244e0c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 582.0000000

Root relaxation: objective 7.040000e+02, 46 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     704.0000000  704.00000  0.00%     -    0s

Explored 1 nodes (46 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 704 582 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 7.040000000000e+02, best bound 7.040000000000e+02, gap 0.0000%
=================== for P=5
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xd5c0d085
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 675.0000000

Root relaxation: objective 8.550000e+02, 43 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     855.0000000  855.00000  0.00%     -    0s

Explored 1 nodes (43 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 855 675 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 8.550000000000e+02, best bound 8.550000000000e+02, gap 0.0000%
=================== for P=6
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe2dcaec6
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 746.0000000

Root relaxation: objective 1.005000e+03, 39 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1005.0000000 1005.00000  0.00%     -    0s

Explored 1 nodes (39 simplex iterations) in 0.09 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1005 746 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.005000000000e+03, best bound 1.005000000000e+03, gap 0.0000%
=================== for P=7
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x03031656
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 929.0000000

Root relaxation: objective 1.146000e+03, 38 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1146.0000000 1146.00000  0.00%     -    0s

Explored 1 nodes (38 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1146 929 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.146000000000e+03, best bound 1.146000000000e+03, gap 0.0000%
=================== for P=8
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe1716b61
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1086.0000000

Root relaxation: objective 1.270000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1270.0000000 1270.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1270 1086 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.270000000000e+03, best bound 1.270000000000e+03, gap 0.0000%
=================== for P=9
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x0064714e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1177.0000000

Root relaxation: objective 1.384000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1384.0000000 1384.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1384 1177 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.384000000000e+03, best bound 1.384000000000e+03, gap 0.0000%
=================== for P=10
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x59a2cd6c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1291.0000000

Root relaxation: objective 1.475000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1475.0000000 1475.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1475 1291 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.475000000000e+03, best bound 1.475000000000e+03, gap 0.0000%
=================== for P=11
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x09995fa2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1433.0000000

Root relaxation: objective 1.564000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1564.0000000 1564.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1564 1433 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.564000000000e+03, best bound 1.564000000000e+03, gap 0.0000%
=================== for P=12
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x76eb931e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1493.0000000

Root relaxation: objective 1.647000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1647.0000000 1647.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1647 1493 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.647000000000e+03, best bound 1.647000000000e+03, gap 0.0000%
=================== for P=13
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9f43fd0d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1591.0000000

Root relaxation: objective 1.715000e+03, 18 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1715.0000000 1715.00000  0.00%     -    0s

Explored 1 nodes (18 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1715 1591 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.715000000000e+03, best bound 1.715000000000e+03, gap 0.0000%
=================== for P=14
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x96e00db9
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1611.0000000

Root relaxation: objective 1.743000e+03, 17 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1743.0000000 1743.00000  0.00%     -    0s

Explored 1 nodes (17 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1743 1611 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.743000000000e+03, best bound 1.743000000000e+03, gap 0.0000%
=================== for P=15
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xb856d7f5
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1646.0000000

Root relaxation: objective 1.763000e+03, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1763.0000000 1763.00000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1763 1646 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.763000000000e+03, best bound 1.763000000000e+03, gap 0.0000%
=================== for P=16
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x850efa85
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1714.0000000

Root relaxation: objective 1.780000e+03, 8 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1780.0000000 1780.00000  0.00%     -    0s

Explored 1 nodes (8 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1780 1714 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.780000000000e+03, best bound 1.780000000000e+03, gap 0.0000%
=================== for P=17
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x924aa403
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1789.0000000

Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0     cutoff    0      1789.00000 1789.00000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1789 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.789000000000e+03, best bound 1.789000000000e+03, gap 0.0000%
=================== for P=18
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9fdd0b2d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1793.0000000

Root relaxation: infeasible, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0 infeasible    0      1793.00000 1793.00000  0.00%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1793 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.793000000000e+03, best bound 1.793000000000e+03, gap 0.0000%
=================== for P=19
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xbefdbbc8
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1797.0000000

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=20
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xc70b4648
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3261 rows and 6540 columns
Presolve time: 0.02s
Presolved: 44 rows, 68 columns, 192 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 68 integer (68 binary)

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=21
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xc686342d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3264 rows and 6543 columns
Presolve time: 0.01s
Presolved: 41 rows, 65 columns, 174 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 65 integer (65 binary)

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=22
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x1cd35457
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3272 rows and 6551 columns
Presolve time: 0.01s
Presolved: 33 rows, 57 columns, 134 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 57 integer (57 binary)

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=23
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x252332b2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3285 rows and 6564 columns
Presolve time: 0.01s
Presolved: 20 rows, 44 columns, 82 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 44 integer (44 binary)

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=24
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x69bf8981
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=25
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xa3528c1e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=26
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x6841d82b
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=27
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x027cece1
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.02s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=28
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x1d894e10
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

optimize_and_evaluate(demand_block=False)

=================== for P=3
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x389340da
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 506.0000000

Root relaxation: objective 5.400000e+02, 45 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     540.0000000  540.00000  0.00%     -    0s

Explored 1 nodes (45 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 540 506 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 5.400000000000e+02, best bound 5.400000000000e+02, gap 0.0000%

=================== for P=4
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x7e244e0c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 582.0000000

Root relaxation: objective 7.040000e+02, 46 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     704.0000000  704.00000  0.00%     -    0s

Explored 1 nodes (46 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 704 582 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 7.040000000000e+02, best bound 7.040000000000e+02, gap 0.0000%

=================== for P=5
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xd5c0d085
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 675.0000000

Root relaxation: objective 8.550000e+02, 43 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     855.0000000  855.00000  0.00%     -    0s

Explored 1 nodes (43 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 855 675 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 8.550000000000e+02, best bound 8.550000000000e+02, gap 0.0000%

=================== for P=6
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe2dcaec6
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 746.0000000

Root relaxation: objective 1.005000e+03, 39 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1005.0000000 1005.00000  0.00%     -    0s

Explored 1 nodes (39 simplex iterations) in 0.08 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1005 746 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.005000000000e+03, best bound 1.005000000000e+03, gap 0.0000%

=================== for P=7
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x03031656
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 929.0000000

Root relaxation: objective 1.146000e+03, 38 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1146.0000000 1146.00000  0.00%     -    0s

Explored 1 nodes (38 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1146 929 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.146000000000e+03, best bound 1.146000000000e+03, gap 0.0000%

=================== for P=8
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe1716b61
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.03s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1086.0000000

Root relaxation: objective 1.270000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1270.0000000 1270.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.09 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1270 1086 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.270000000000e+03, best bound 1.270000000000e+03, gap 0.0000%

=================== for P=9
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x0064714e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1177.0000000

Root relaxation: objective 1.384000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1384.0000000 1384.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1384 1177 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.384000000000e+03, best bound 1.384000000000e+03, gap 0.0000%

=================== for P=10
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x59a2cd6c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1291.0000000

Root relaxation: objective 1.475000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1475.0000000 1475.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1475 1291 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.475000000000e+03, best bound 1.475000000000e+03, gap 0.0000%

=================== for P=11
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x09995fa2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1433.0000000

Root relaxation: objective 1.564000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1564.0000000 1564.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1564 1433 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.564000000000e+03, best bound 1.564000000000e+03, gap 0.0000%

=================== for P=12
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x76eb931e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1493.0000000

Root relaxation: objective 1.647000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1647.0000000 1647.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1647 1493 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.647000000000e+03, best bound 1.647000000000e+03, gap 0.0000%

=================== for P=13
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9f43fd0d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1591.0000000

Root relaxation: objective 1.715000e+03, 18 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1715.0000000 1715.00000  0.00%     -    0s

Explored 1 nodes (18 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1715 1591 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.715000000000e+03, best bound 1.715000000000e+03, gap 0.0000%

=================== for P=14
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x96e00db9
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1611.0000000

Root relaxation: objective 1.743000e+03, 17 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1743.0000000 1743.00000  0.00%     -    0s

Explored 1 nodes (17 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1743 1611 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.743000000000e+03, best bound 1.743000000000e+03, gap 0.0000%

=================== for P=15
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xb856d7f5
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1646.0000000

Root relaxation: objective 1.763000e+03, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1763.0000000 1763.00000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1763 1646 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.763000000000e+03, best bound 1.763000000000e+03, gap 0.0000%

=================== for P=16
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x850efa85
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1714.0000000

Root relaxation: objective 1.780000e+03, 8 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1780.0000000 1780.00000  0.00%     -    0s

Explored 1 nodes (8 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1780 1714 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.780000000000e+03, best bound 1.780000000000e+03, gap 0.0000%

=================== for P=17
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x924aa403
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1789.0000000

Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0     cutoff    0      1789.00000 1789.00000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1789 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.789000000000e+03, best bound 1.789000000000e+03, gap 0.0000%

=================== for P=18
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9fdd0b2d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1793.0000000

Root relaxation: infeasible, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0 infeasible    0      1793.00000 1793.00000  0.00%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1793 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.793000000000e+03, best bound 1.793000000000e+03, gap 0.0000%

=================== for P=19
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xbefdbbc8
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1797.0000000

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=20
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xc70b4648
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3261 rows and 6540 columns
Presolve time: 0.01s
Presolved: 44 rows, 68 columns, 192 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 68 integer (68 binary)

Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=21
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xc686342d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3264 rows and 6543 columns
Presolve time: 0.02s
Presolved: 41 rows, 65 columns, 174 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 65 integer (65 binary)

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=22
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x1cd35457
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3272 rows and 6551 columns
Presolve time: 0.01s
Presolved: 33 rows, 57 columns, 134 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 57 integer (57 binary)

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=23
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x252332b2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3285 rows and 6564 columns
Presolve time: 0.01s
Presolved: 20 rows, 44 columns, 82 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 44 integer (44 binary)

Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=24
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x69bf8981
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.02s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=25
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xa3528c1e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=26
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x6841d82b
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=27
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x027cece1
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=28
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x1d894e10
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

Task: Repeat the whole process with another fishnet_points with different fishnet interval.

interval = 5280  # default: 5280/5 feet (1 mile / 5 = 0.2 mile) 
fishnet_points = create_fishnet(interval)

Number of points in the fishnet: 330

selecteds = []  # List to store selected stations for each value of p
obj_vals = []   # List to store objective values for each value of p

# Iterate over values of p starting from 3
for p in range(3, len(stations)+1):
    print(f"=================== for P={p}")  # Print current value of p
    # Call solve_mclp function to solve the problem for current value of p
    selected_stations, obj_val = solve_mclp(p)
    # Append selected stations to the selecteds list
    selecteds.append(selected_stations)
    # Append objective value to the obj_vals list
    obj_vals.append(obj_val)

=================== for P=3
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x389340da
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 506.0000000

Root relaxation: objective 5.400000e+02, 45 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     540.0000000  540.00000  0.00%     -    0s

Explored 1 nodes (45 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 540 506 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 5.400000000000e+02, best bound 5.400000000000e+02, gap 0.0000%
=================== for P=4
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x7e244e0c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 582.0000000

Root relaxation: objective 7.040000e+02, 46 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     704.0000000  704.00000  0.00%     -    0s

Explored 1 nodes (46 simplex iterations) in 0.08 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 704 582 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 7.040000000000e+02, best bound 7.040000000000e+02, gap 0.0000%
=================== for P=5
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xd5c0d085
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.03s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 675.0000000

Root relaxation: objective 8.550000e+02, 43 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     855.0000000  855.00000  0.00%     -    0s

Explored 1 nodes (43 simplex iterations) in 0.10 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 855 675 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 8.550000000000e+02, best bound 8.550000000000e+02, gap 0.0000%
=================== for P=6
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe2dcaec6
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.03s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 746.0000000

Root relaxation: objective 1.005000e+03, 39 iterations, 0.01 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1005.0000000 1005.00000  0.00%     -    0s

Explored 1 nodes (39 simplex iterations) in 0.13 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1005 746 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.005000000000e+03, best bound 1.005000000000e+03, gap 0.0000%
=================== for P=7
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x03031656
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 929.0000000

Root relaxation: objective 1.146000e+03, 38 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1146.0000000 1146.00000  0.00%     -    0s

Explored 1 nodes (38 simplex iterations) in 0.19 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1146 929 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.146000000000e+03, best bound 1.146000000000e+03, gap 0.0000%
=================== for P=8
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe1716b61
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1086.0000000

Root relaxation: objective 1.270000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1270.0000000 1270.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1270 1086 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.270000000000e+03, best bound 1.270000000000e+03, gap 0.0000%
=================== for P=9
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x0064714e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1177.0000000

Root relaxation: objective 1.384000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1384.0000000 1384.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.08 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1384 1177 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.384000000000e+03, best bound 1.384000000000e+03, gap 0.0000%
=================== for P=10
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x59a2cd6c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1291.0000000

Root relaxation: objective 1.475000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1475.0000000 1475.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1475 1291 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.475000000000e+03, best bound 1.475000000000e+03, gap 0.0000%
=================== for P=11
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x09995fa2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1433.0000000

Root relaxation: objective 1.564000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1564.0000000 1564.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1564 1433 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.564000000000e+03, best bound 1.564000000000e+03, gap 0.0000%
=================== for P=12
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x76eb931e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1493.0000000

Root relaxation: objective 1.647000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1647.0000000 1647.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1647 1493 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.647000000000e+03, best bound 1.647000000000e+03, gap 0.0000%
=================== for P=13
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9f43fd0d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1591.0000000

Root relaxation: objective 1.715000e+03, 18 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1715.0000000 1715.00000  0.00%     -    0s

Explored 1 nodes (18 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1715 1591 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.715000000000e+03, best bound 1.715000000000e+03, gap 0.0000%
=================== for P=14
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x96e00db9
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1611.0000000

Root relaxation: objective 1.743000e+03, 17 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1743.0000000 1743.00000  0.00%     -    0s

Explored 1 nodes (17 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1743 1611 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.743000000000e+03, best bound 1.743000000000e+03, gap 0.0000%
=================== for P=15
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xb856d7f5
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1646.0000000

Root relaxation: objective 1.763000e+03, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1763.0000000 1763.00000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1763 1646 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.763000000000e+03, best bound 1.763000000000e+03, gap 0.0000%
=================== for P=16
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x850efa85
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1714.0000000

Root relaxation: objective 1.780000e+03, 8 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1780.0000000 1780.00000  0.00%     -    0s

Explored 1 nodes (8 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1780 1714 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.780000000000e+03, best bound 1.780000000000e+03, gap 0.0000%
=================== for P=17
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x924aa403
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1789.0000000

Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0     cutoff    0      1789.00000 1789.00000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.10 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1789 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.789000000000e+03, best bound 1.789000000000e+03, gap 0.0000%
=================== for P=18
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9fdd0b2d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1793.0000000

Root relaxation: infeasible, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0 infeasible    0      1793.00000 1793.00000  0.00%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1793 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.793000000000e+03, best bound 1.793000000000e+03, gap 0.0000%
=================== for P=19
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xbefdbbc8
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.04s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1797.0000000

Explored 0 nodes (0 simplex iterations) in 0.12 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=20
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xc70b4648
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3261 rows and 6540 columns
Presolve time: 0.02s
Presolved: 44 rows, 68 columns, 192 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 68 integer (68 binary)

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=21
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xc686342d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3264 rows and 6543 columns
Presolve time: 0.02s
Presolved: 41 rows, 65 columns, 174 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 65 integer (65 binary)

Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=22
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x1cd35457
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3272 rows and 6551 columns
Presolve time: 0.01s
Presolved: 33 rows, 57 columns, 134 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 57 integer (57 binary)

Explored 0 nodes (0 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=23
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x252332b2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3285 rows and 6564 columns
Presolve time: 0.01s
Presolved: 20 rows, 44 columns, 82 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 44 integer (44 binary)

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=24
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x69bf8981
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.15 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=25
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xa3528c1e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=26
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x6841d82b
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=27
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x027cece1
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=28
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x1d894e10
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

optimize_and_evaluate(demand_block=False)

=================== for P=3
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x389340da
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 506.0000000

Root relaxation: objective 5.400000e+02, 45 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     540.0000000  540.00000  0.00%     -    0s

Explored 1 nodes (45 simplex iterations) in 0.15 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 540 506 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 5.400000000000e+02, best bound 5.400000000000e+02, gap 0.0000%

=================== for P=4
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x7e244e0c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.03s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 582.0000000

Root relaxation: objective 7.040000e+02, 46 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     704.0000000  704.00000  0.00%     -    0s

Explored 1 nodes (46 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 704 582 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 7.040000000000e+02, best bound 7.040000000000e+02, gap 0.0000%

=================== for P=5
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xd5c0d085
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 675.0000000

Root relaxation: objective 8.550000e+02, 43 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     855.0000000  855.00000  0.00%     -    0s

Explored 1 nodes (43 simplex iterations) in 0.08 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 855 675 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 8.550000000000e+02, best bound 8.550000000000e+02, gap 0.0000%

=================== for P=6
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe2dcaec6
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 746.0000000

Root relaxation: objective 1.005000e+03, 39 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1005.0000000 1005.00000  0.00%     -    0s

Explored 1 nodes (39 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1005 746 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.005000000000e+03, best bound 1.005000000000e+03, gap 0.0000%

=================== for P=7
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x03031656
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 929.0000000

Root relaxation: objective 1.146000e+03, 38 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1146.0000000 1146.00000  0.00%     -    0s

Explored 1 nodes (38 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1146 929 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.146000000000e+03, best bound 1.146000000000e+03, gap 0.0000%

=================== for P=8
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe1716b61
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1086.0000000

Root relaxation: objective 1.270000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1270.0000000 1270.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1270 1086 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.270000000000e+03, best bound 1.270000000000e+03, gap 0.0000%

=================== for P=9
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x0064714e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1177.0000000

Root relaxation: objective 1.384000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1384.0000000 1384.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1384 1177 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.384000000000e+03, best bound 1.384000000000e+03, gap 0.0000%

=================== for P=10
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x59a2cd6c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1291.0000000

Root relaxation: objective 1.475000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1475.0000000 1475.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1475 1291 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.475000000000e+03, best bound 1.475000000000e+03, gap 0.0000%

=================== for P=11
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x09995fa2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1433.0000000

Root relaxation: objective 1.564000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1564.0000000 1564.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1564 1433 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.564000000000e+03, best bound 1.564000000000e+03, gap 0.0000%

=================== for P=12
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x76eb931e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1493.0000000

Root relaxation: objective 1.647000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1647.0000000 1647.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1647 1493 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.647000000000e+03, best bound 1.647000000000e+03, gap 0.0000%

=================== for P=13
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9f43fd0d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1591.0000000

Root relaxation: objective 1.715000e+03, 18 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1715.0000000 1715.00000  0.00%     -    0s

Explored 1 nodes (18 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1715 1591 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.715000000000e+03, best bound 1.715000000000e+03, gap 0.0000%

=================== for P=14
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x96e00db9
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1611.0000000

Root relaxation: objective 1.743000e+03, 17 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1743.0000000 1743.00000  0.00%     -    0s

Explored 1 nodes (17 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1743 1611 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.743000000000e+03, best bound 1.743000000000e+03, gap 0.0000%

=================== for P=15
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xb856d7f5
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1646.0000000

Root relaxation: objective 1.763000e+03, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1763.0000000 1763.00000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1763 1646 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.763000000000e+03, best bound 1.763000000000e+03, gap 0.0000%

=================== for P=16
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x850efa85
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1714.0000000

Root relaxation: objective 1.780000e+03, 8 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1780.0000000 1780.00000  0.00%     -    0s

Explored 1 nodes (8 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 3: 1780 1714 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.780000000000e+03, best bound 1.780000000000e+03, gap 0.0000%

=================== for P=17
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x924aa403
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1789.0000000

Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0     cutoff    0      1789.00000 1789.00000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1789 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.789000000000e+03, best bound 1.789000000000e+03, gap 0.0000%

=================== for P=18
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9fdd0b2d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1793.0000000

Root relaxation: infeasible, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0 infeasible    0      1793.00000 1793.00000  0.00%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1793 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.793000000000e+03, best bound 1.793000000000e+03, gap 0.0000%

=================== for P=19
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xbefdbbc8
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1797.0000000

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=20
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xc70b4648
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3261 rows and 6540 columns
Presolve time: 0.01s
Presolved: 44 rows, 68 columns, 192 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 68 integer (68 binary)

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=21
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xc686342d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3264 rows and 6543 columns
Presolve time: 0.02s
Presolved: 41 rows, 65 columns, 174 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 65 integer (65 binary)

Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=22
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x1cd35457
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3272 rows and 6551 columns
Presolve time: 0.02s
Presolved: 33 rows, 57 columns, 134 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 57 integer (57 binary)

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=23
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x252332b2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3285 rows and 6564 columns
Presolve time: 0.01s
Presolved: 20 rows, 44 columns, 82 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 44 integer (44 binary)

Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=24
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x69bf8981
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=25
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xa3528c1e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=26
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x6841d82b
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=27
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x027cece1
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

=================== for P=28
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])

CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads

Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x1d894e10
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%

Question 10: Compare the Scatter plots out of Blocks, 0.2 mile fishnet points, and another fishnet points with interval of your choice. Discuss the insights you can get. ( 5 pts )

In Lab 2, we discovered that different Coverage Distance Standard can impact the coverage analysis result.
In Lab 4, we can discover how different demand representation makes difference.
Share your insights about

• provide three scatter plots ( 3 pts )
• how SBC_FD is currently doing with existing stations in terms of coverage ( 1 pt )
• how demand representation impacts the coverage analysis ( 1 pt )

TIP: you can copy and paste your screenshot into markdown cells

PUT your answer HERE

1. Current coverage by SBC_FD is excellent in terms of pure coverage, but not so well in terms of cost efficiency. The current coverage is at the end of the Pareto curve shown in scatter plot 1. This means that they are using far more stations than they need to for the coverage they are providing. This can be seen in the flattening of the curve as it approaches the current coverage level. They could reduce the number of stations and get the same amount of coverage and save millions of dollars a year.

2. When the demand representation was defined using population, there were many overlapping stations placed on the downtown SB area and other population dense regions. At the same time, these coverage areas were not spatially optimized in the sense that many of them were overlapping in order to cover larger populations. When we optimized based on a maximization of fishnet points the locations were largely organized in the middle of the county. This makes sense give that there are the most fishnet points in the center as opposed to coastlines or other more complex regions.